Applications of Alternating Direction Solver for simulations of time-dependent problems

Marcin Mateusz Łoś, Maciej Paszyński

Abstract


This paper deals with application of Alternating Direction solver (ADS) to nonstationary
linear elasticity problem solved with isogeometric FEM. Employing
tensor product B-spline basis in isogeometric analysis under some restrictions
leads to system of linear equations with matrix possessing tensor product structure.
Alternating Direction Implicit algorithm is a direct method that exploits
this structure to solve the system in O (N ), where N is a number of degrees
of freedom (basis functions). This is asymptotically faster than state-of-theart
general purpose multi-frontal direct solvers. In this paper we also present
the complexity analysis of ADS incorporating dependence on order of B-spline
basis.


Keywords


FEM; Isogeometric Analysis; Alternating Direction Solver

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References


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DOI: https://doi.org/10.7494/csci.2017.18.2.117

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